Spatial-Temporal Modeling and Computation for Physical Processes and Numerical Simulations

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Every minute of every day, a swarm of satellites captures images of the scenes below, and supercomputers churn out simulations of future weather and climate, accumulating a mountain of raw information about the Earth and its atmosphere. Since a significant amount of public funding has been devoted to the collection and production of this data, it is imperative that statistical tools be up to the task of analyzing it. This project aims to sort through this information, accurately filling in gaps in the raw data, inferring meaningful quantities--such as changing wind patterns--from sequences of images, and refining our understanding of the Earth as an interconnected system through the analysis of numerical computer simulations. Statistical techniques developed during this project will be made accessible to the broader community by public dissemination of software. Students and emerging researchers will be trained to use the new methods and will be empowered with specific knowledge and independent critical thinking skills to venture out and make their own impacts.The project outlines advancements for three crucial tasks in the geoscientific data analysis pipeline. (1) Observations from ground monitors and polar orbiting satellites often have gaps in space and time that must be interpolated. Thus, new Gaussian process approximations are proposed that significantly reduce computational effort while improving approximations, allowing for fast and accurate interpolations. (2) Geostationary satellite sensors afford the opportunity for fine scale, continual monitoring of the atmosphere. This proposal outlines a framework for using these data--which consist of a temporal sequence of images--for the purpose of inferring upper air wind fields. (3) The pace of supercomputing has continued to increase our ability to produce high-resolution numerical simulations, which requires new computational tools for analyzing the output. A technique is proposed for local estimation that results in a globally valid statistical model, a critical feature that enables numerical model emulation and data compression via statistical models.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.